{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "850bd85a-8727-4eb9-bc02-a3cceb4a3b10",
   "metadata": {},
   "source": [
    "- batch size 越大，相应地 learning rate 也越大\n",
    "    - When the minibatch size is multiplied by k, multiply the learning rate by k.\n",
    "        - https://arxiv.org/pdf/1706.02677.pdf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "f6f921f7-93d4-4194-9f44-344e52770d6c",
   "metadata": {},
   "outputs": [],
   "source": [
    "from tqdm.notebook import tqdm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "9dc06ecb-2722-4586-bc43-b8c4d13b87bc",
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "import torch.nn as nn\n",
    "import torch.optim as optim\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Ensure reproducibility\n",
    "torch.manual_seed(0)\n",
    "np.random.seed(0)\n",
    "\n",
    "# Creating a synthetic dataset for a simple regression problem\n",
    "X = np.random.rand(1000, 10)\n",
    "y = np.dot(X, np.random.rand(10, 1)) + np.random.rand(1000, 1)\n",
    "X = torch.tensor(X, dtype=torch.float32)\n",
    "y = torch.tensor(y, dtype=torch.float32)\n",
    "\n",
    "# Defining a simple neural network model for the regression task\n",
    "class SimpleNN(nn.Module):\n",
    "    def __init__(self, input_size):\n",
    "        super(SimpleNN, self).__init__()\n",
    "        self.fc1 = nn.Linear(input_size, 64)\n",
    "        self.relu = nn.ReLU()\n",
    "        self.fc2 = nn.Linear(64, 32)\n",
    "        self.fc3 = nn.Linear(32, 1)\n",
    "\n",
    "    def forward(self, x):\n",
    "        x = self.relu(self.fc1(x))\n",
    "        x = self.relu(self.fc2(x))\n",
    "        x = self.fc3(x)\n",
    "        return x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "bbb20abb-b42f-4897-9d0b-2e5094af8fa8",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Training configurations\n",
    "batch_sizes = [16, 32, 64, 128, 256]\n",
    "learning_rates = [0.1, 0.01, 0.001, 0.0001]\n",
    "epochs = 50\n",
    "\n",
    "# Dictionary to store training results\n",
    "results = {}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "ea4e15a6-6890-4a84-abcf-215b098ddff7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "72f6676d542e42ad9ff95582346bede8",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "ca2dbe183de548fb979d51df8ab5bbd9",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "b4f146ed2f6a451ca5a083b5fa0943d2",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/4 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "3396779c1ad244d0a0c439597cf94cb7",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "e68bc3627ff148bea02e8ee1b455ea8d",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/4 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "ac07acdaa383418a89e702b240e67d0c",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/4 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Training the model with different batch sizes and learning rates\n",
    "for batch_size in tqdm(batch_sizes):\n",
    "    for lr in tqdm(learning_rates):\n",
    "        # Create a new instance of the model\n",
    "        model = SimpleNN(X.shape[1])\n",
    "        \n",
    "        # Compile the model with the current learning rate\n",
    "        optimizer = optim.Adam(model.parameters(), lr=lr)\n",
    "        criterion = nn.MSELoss()\n",
    "\n",
    "        # Dataset loader\n",
    "        dataset = torch.utils.data.TensorDataset(X, y)\n",
    "        dataloader = torch.utils.data.DataLoader(dataset, batch_size=batch_size, shuffle=True)\n",
    "        \n",
    "        # Train the model\n",
    "        model.train()\n",
    "        for epoch in range(epochs):\n",
    "            for data, target in dataloader:\n",
    "                optimizer.zero_grad()\n",
    "                output = model(data)\n",
    "                loss = criterion(output, target)\n",
    "                loss.backward()\n",
    "                optimizer.step()\n",
    "        \n",
    "        # Store the training results\n",
    "        results[(batch_size, lr)] = loss.item()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "10523857-5f30-45dc-bfda-f77b57655e02",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Converting results to a more plot-friendly format\n",
    "plot_data = {f'LR: {lr}': [results[(bs, lr)] for bs in batch_sizes] for lr in learning_rates}\n",
    "\n",
    "# Plotting the results\n",
    "plt.figure(figsize=(10, 6))\n",
    "for lr, losses in plot_data.items():\n",
    "    plt.plot(batch_sizes, losses, marker='o', label=lr)\n",
    "\n",
    "plt.title('Effect of Batch Size and Learning Rate on Final Loss')\n",
    "plt.xlabel('Batch Size')\n",
    "plt.ylabel('Final Loss')\n",
    "plt.xscale('log')\n",
    "plt.yscale('log')\n",
    "plt.legend()\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
